The Impact of Consumption on an Investor’s Strategy under Stochastic Interest Rate and Correlating Brownian Motions | Chapter 02 | Advances in Mathematics and Computer Science Vol. 4

In this work, we consider that an investor’s portfolio comprises of two assets- a risk-free asset driven by Ornstein-Uhlenbeck Stochastic interest rate of return model and the second asset a risky stock with a price process governed by the geometric Brownian motion. It is also considered that there are withdrawals for consumption and taxes, transaction costs and dividends are in involved. The aim was to investigate the effect of consumption on an investor’s trading strategy under correlating Brownian motions. The relating Hamilton-Jacobi-Bellman (HJB) equation was obtained using maximum principle. The application of elimination of variable dependency gave the optimal investment strategy for the investor’s problem. Among the findings is that more fund should be made available for investment on the risky asset when there is consumption to keep the investor solvent.

Author(s) Details

Silas A. Ihedioha
Department of Mathematics, Plateau State University Bokkos, P.M.B. 2012, Jos, Plateau State, Nigeria.

Ubani, Sunday Iheanyi
Federal College of Agriculture, Ishiagu, Ebonyi State, Nigeria.

Njoku, Iheanyi Odochi
Federal College of Agriculture, Ishiagu, Ebonyi State, Nigeria.

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Investor’s Power Utility Optimization with Consumption, Tax, Dividend and Transaction Cost under Constant Elasticity of Variance Model | Chapter 07 | Advances in Mathematics and Computer Science Vol. 3

This work considered an investor’s portfolio where consumption, taxes, transaction costs and dividends are in involved, under constant elasticity of variance (CEV). The stock price is assumed to be governed by a constant elasticity of variance CEV model and the goal is to maximize the expected utility of consumption and terminal wealth where the investor has a power utility preference. The application of dynamic programming principles, specifically the maximum principle obtained the Hamilton Jacobi-Bellman (HJB) equation for the value function on which elimination of variable dependency was applied to obtain the close form solution of the optimal investment and consumption strategies. It is found that optimal investment on the risky asset is horizon dependent.

Author(s) Details

Silas A. Ihedioha
Department of Mathematics, Plateau State University, Bokkos, P.M.B. 2012, Jos, Plateau State, Nigeria.

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View Volume: https://doi.org/10.9734/bpi/amacs/v3